.TH "SRC/chptrd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/chptrd.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBchptrd\fP (uplo, n, ap, d, e, tau, info)"
.br
.RI "\fBCHPTRD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine chptrd (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( * ) tau, integer info)"

.PP
\fBCHPTRD\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
 CHPTRD reduces a complex Hermitian matrix A stored in packed form to
 real symmetric tridiagonal form T by a unitary similarity
 transformation: Q**H * A * Q = T\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX array, dimension (N*(N+1)/2)
          On entry, the upper or lower triangle of the Hermitian matrix
          A, packed columnwise in a linear array\&.  The j-th column of A
          is stored in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n\&.
          On exit, if UPLO = 'U', the diagonal and first superdiagonal
          of A are overwritten by the corresponding elements of the
          tridiagonal matrix T, and the elements above the first
          superdiagonal, with the array TAU, represent the unitary
          matrix Q as a product of elementary reflectors; if UPLO
          = 'L', the diagonal and first subdiagonal of A are over-
          written by the corresponding elements of the tridiagonal
          matrix T, and the elements below the first subdiagonal, with
          the array TAU, represent the unitary matrix Q as a product
          of elementary reflectors\&. See Further Details\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          The diagonal elements of the tridiagonal matrix T:
          D(i) = A(i,i)\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (N-1)
          The off-diagonal elements of the tridiagonal matrix T:
          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX array, dimension (N-1)
          The scalar factors of the elementary reflectors (see Further
          Details)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  If UPLO = 'U', the matrix Q is represented as a product of elementary
  reflectors

     Q = H(n-1) \&. \&. \&. H(2) H(1)\&.

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
  overwriting A(1:i-1,i+1), and tau is stored in TAU(i)\&.

  If UPLO = 'L', the matrix Q is represented as a product of elementary
  reflectors

     Q = H(1) H(2) \&. \&. \&. H(n-1)\&.

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
  overwriting A(i+2:n,i), and tau is stored in TAU(i)\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB150\fP of file \fBchptrd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.